Astrophysics question re. spacetime curvature

[0rganism]

OK, now maybe this is a simple question, and I'm just thinking about it all mixed up. But it's been bugging me lately (too many Hubble telescope pictures I guess), and I know there are a few competent physics folk on this board, so here goes.

1) Standard "inflation" cosmology posits that the universe expands from a singularity.

2) Light (and other E-M) travels at a finite speed; the farther away something appears, the "older" it is.

3) Thus, if the Hubble limit were to somehow "catch up" to the point where we could see EM from the beginning of time, we would be looking back at the same point from all directions.

4) Spacetime seems therefore be curved, in the manner of a sphere, but 4-dimensional; similarly, any way you travel "North", you're going towards the North pole but only if you follow the curvature of the earth.

5) So here's the situation:

X is the singularity event
O is the Observer planet (Earth?)
Ed and Fred are looking into space with their telescopes 
from the north and south poles, respectively....
                      Ed
         X---------<----O--->---------X
                          Fred
Both see X, by looking far enough into the past from 
opposite directions.  But X is a singularity! 
                   Ed
         /------<----O--->------\
         |             Fred     |
         v                      v
         |                      |
         \------>----X----<-----/

6) So couldn't we quantify, based on the "age" of the universe and the angular limit to which we could look "back in time" to see the same light repeated, just how curved space is in terms of radians per light-year, or some such?

7) A thought experiment, then: suppose you're living on a planet in a smaller universe which stopped expanding after, say, 10 years. Its Omega constant is 1.0, which IIRC means it reaches a stable inflationary state. You look out into space with your telescope and see the singularity after 10 years. 10 years after that, if you looked into the telescope again, you could see YOURSELF looking back at you 10 years ago! Is this an accurate description?

[htuttle]

1. I think the universe is too large for #3 to be possible

As I understand it, as a lay person, things that are farther from us are receeding faster from us (ie., the 'dots on the expanding balloon' demonstration). At some distance, I believe that space would be expanding relative to us as fast (or faster) than the speed of light. Light from things that far away could therefore never possibly reach us. Note: SPACE would be expanding relative to us faster than the speed of light. Matter wouldn't traveling faster than light relative to the space it 'occupies', so I think this is possible.

Regarding point #7: you would be looking at the center of the universe 10 years previous, no matter when you looked (ie., at 40 years, you'd be looking at the center of the universe at 30 years old). I think.

[0rganism]

3. Perhaps. I guess the overall model is more what tickles me

As I understand it, we don't know the actual Omega constant for our universe, as it would depend on hard-to-measure "dark matter". But if we were in either a stable or eventually-contracting universe, it seems to me that the Hubble limit would eventually catch up with the center point.

Now having Ed and Fred at the poles is kind of the extreme case, but it seems to me that initially the observation angle would become a gradually increasing cone-shape, in which one eventually sees the same points from increasingly wide angles.

Point #7 is kind of a funny one. I'm trying to imagine tho, if you have a radiating or reflective body emitting in all directions, and the EM waves follow the curvature of space, do they stop at the singularity or radiate right on past it for a second pass? And a third? And a fourth?

[dave29]

2. Couple of things

1) singularity - the Big Bang singularity is often confused with a "black hole" singularity. While a black hole singularity has a specific location in space, the Big Bang "singularity" included all of spacetime. Some theorize that the Big Bang event is more like a "White Hole".

http://www.space.com/scienceastronomy/white_hole_030917.html

2)There is also speculation that the speed of light is actually changing over time.

http://curious.astro.cornell.edu/question.php?number=606

3) Dark Energy - recently it was discovered that Dark Energy is actually causing an increase in the rate of expansion of the Universe.

http://universe.gsfc.nasa.gov/science/darkenergy.html

[Westegg]

4. So, in other words (this is a question for smart guys like you)

...Time travel is theoretically possible.

[Dudley_DUright]

7. Theoretically possible, but only if wormholes could be created

and stablized with negative energy. However, we have no idea how to do this. The following Popular Science article gives a good summary of some of the ideas of Kip Thorne, Cal Tech professor of physics.

http://www.popsci.com/popsci/science/article/0,12543,211498-1,00.html

[0rganism]

8. Or if you can line up some pulsars...

Frank Tipler's time machine theory uses a cylinder of spinning neutron star material to radically warp spacetime with gravity. You could approximate the cylinder by a row of pulsars -- if you could keep them from collapsing on one-another. Anyway, the idea was you'd travel parallel to the cylinder's axis, but what seemed like a spatial axis to the traveler would seem like a temporal axis to the observer.

Isn't it kind of funny that objects which resemble potential components of Tipler's time machine occur "naturally" in the universe?

[Dudley_DUright]

10. I had not heard about Tipler's idea

I will have to look it up.

[dave29]

9. my favorite response to this is

you are travelling through time right now ;) - more smartass than smart, huh.

Time travel:

This is debatable - but I take the glass half-full approach and think that just about anything you imagine can be made possible. Most scientists do not agree - and we are certainly a long ways off with current science (just touching the edge of superluminal communications - and quantum entanglement, which Einstein referred to as "spooky action at a distance"). If information can travel faster than light, why can't we, right?

http://en.wikipedia.org/wiki/Quantum_entanglement
http://www.freep.com/tech/qbeam23.htm

More interestingly for me at this point is the nature of time itself - and the recent assertions (or re-assertions on the subject depending on your level of snarkiness) by Peter Lynds that there is no such thing as an instant in time, since if you slowed time down to an instant, motion would be impossible - and we are clearly in a dynamic universe. Keep an eye on Mr. Lynds - he's a young college dropout from New Zealand, who seems to be ridiculously smart.

http://www.space.com/scienceastronomy/time_theory_030806.html
http://www.peterlynds.net.nz/

I've actually exchanged emails with him - so don't fall for the rumors that he is a hoax.

Peter, by the way, doesn't really think time travel is possible.

[Dudley_DUright]

11. But quantum entanglement can't be used to send information

faster than light, so special relativity is still in good shape.

From your reference on quantum entanglement:

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. This leads to correlations between observable physical properties of the systems that are stronger than any classical correlations. As a result, measurements performed on one system may be interpreted as "influencing" other systems entangled with it. However, no information can be transmitted through entanglement.

http://en.wikipedia.org/wiki/Quantum_entanglement

[Dudley_DUright]

5. Excellent points (although I have my doubts about point 2)

Also need to take into account the "inflationary" model of Alan Guth where the length scale of the universe increased exponentially in a very short period of time.

http://www.powersof10.com/powers/people/station_104.html

[SmileyBoy]

6. You'd probably want to ask Dr. Hawking about that one.

I really couldn't answer that.

[Xithras]

12. The universe doesn't expand at 1c

Remember expansion. The universe, by the best current estimates, is somewhere around 15 billion years old, and yet it is also at least 20 billion light years across, and probably far larger. Why? 1) Because the universe can actually expand at up to 2c (1c in each direction) per year. 2) Because it now appears that for a brief period in the early universe, for reasons we can just barely comprehend, the universe expanded far faster than the speed of light.

This is why the sky isn't white at night :)

Also, it is unlikely that we will ever "see" the singularity because of the universes prior high rates of expansion. The universe has been stretched so much that any light generated at its beginning would have been doppler shifted out of existence by the time it reached us. The best we can hope for is to see the formation of the first galaxies, which may bring us within a few hundred million years of B Day, but the light and energy from the bang itself is so stretched and dissipated at this point that it isn't observable as anything other than background radiation.

[DrWeird]

13. You're forgetting relativity.

If Spaceship A takes off from earth at 1c in one direction and Spaceship B takes off from earth at 1c in the opposite direction then relative to each other they are moving apart at 1c.

[htuttle]

15. But if the space between them is expanding at 0.75 in each direction...

Say they are on opposite sides of the universe. Whatever that means...how about 'they are very far apart'.

Wouldn't the actual distance between them potentially be increasing at a rate greater than 1c, thus making them unable to ever 'see' each other (the light from one could never reach the other)?

Each spaceship would still only be moving at it's current speed 'in' space (they could be 'sitting still' for that matter), but they would be essentially moving apart at FTL. Is this right?

[0rganism]

14. I'm finding this Explanation site to be helpful...

http://www.astro.ucla.edu/~wright/cosmo_01.htm

Lots of things to consider. The space-time diagrams are a nice visualization tool.